财务管理(英文第十三版)ch 3_sheena.pptx
- 文档编号:15254640
- 上传时间:2023-07-02
- 格式:PPTX
- 页数:57
- 大小:1.03MB
财务管理(英文第十三版)ch 3_sheena.pptx
《财务管理(英文第十三版)ch 3_sheena.pptx》由会员分享,可在线阅读,更多相关《财务管理(英文第十三版)ch 3_sheena.pptx(57页珍藏版)》请在冰点文库上搜索。
Chapter3,TimeValueofMoney,TheInterestRateSimpleInterestCompoundInterestCompoundingMoreThanOnceperYearAmortizingaLoan,ChapterOutline,BasicDefinition,PresentValueValuetodayofafuturecashflow.,FutureValueAmounttowhichaninvestmentwillgrowafterearninginterest,BasicDefinition,DiscountRateInterestrateusedtocomputepresentvaluesoffuturecashflows.,DiscountFactorPresentvalueofa$1futurepayment.,Obviously,$10,000today.ThereasonisthatthereisTIMEVALUEOFMONEY!
Whichwouldyouprefer-$10,000todayor$10,000in5years?
TheInterestRate,TIMEallowsyoutheopportunitytopostponeconsumptionandearnINTEREST.,WhyisTIMEsuchanimportantelementinyourdecision?
WhyTIME?
CompoundInterestInterestpaid(earned)onanypreviousinterestearned,aswellasontheprincipalborrowed(lent).InterestonInterest,TypesofInterest,SimpleInterestInterestpaid(earned)ononlytheoriginalamount,orprincipal,borrowed(lent).,FormulaSI=P0(i)(n)SI:
SimpleInterestP0:
Deposittoday(t=0)i:
InterestRateperPeriodn:
NumberofTimePeriods,SimpleInterestFormula,SI=P0(i)(n)=$1,000(.07)
(2)=$140,Assumethatyoudeposit$1,000inanaccountearning7%simpleinterestfor2years.Whatistheaccumulatedinterestattheendofthe2ndyear?
SimpleInterestExample,FV=P0+SI=$1,000+$140=$1,140FutureValueisthevalueatsomefuturetimeofapresentamountofmoney,oraseriesofpayments,evaluatedatagiveninterestrate.,WhatistheFutureValue(FV)ofthedeposit?
SimpleInterest(FV),ThePresentValueissimplythe$1,000youoriginallydeposited.Thatisthevaluetoday!
P0=FV-SIPresentValueisthecurrentvalueofafutureamountofmoney,oraseriesofpayments,evaluatedatagiveninterestrate.,WhatisthePresentValue(PV)ofthepreviousproblem?
SimpleInterest(PV),WhyCompoundInterest?
FutureValue(U.S.Dollars),Assumethatyoudeposit$1,000atacompoundinterestrateof7%for2years.,FutureValueSingleDeposit(Graphic),012,$1,000,FV2,7%,FV1=P0(1+i)1=$1,000(1.07)=$1,070CompoundInterestYouearned$70interestonyour$1,000depositoverthefirstyear.Thisisthesameamountofinterestyouwouldearnundersimpleinterest.,FutureValueSingleDeposit(Formula),FV1=P0(1+i)1FV2=P0(1+i)2GeneralFutureValueFormula:
FVn=P0(1+i)norFVn=P0(FVIFi,n)SeeTableI,GeneralFutureValueFormula,FVIFi,nisonTableIattheendofthebook,ValuationUsingTableI,JulieMillerwantstoknowhowlargeherdepositof$10,000todaywillbecomeatacompoundannualinterestrateof10%for5years.,Example,012345,$10,000,FV5,10%,CalculationbasedonTableI:
FV5=$10,000(FVIF10%,5)=$10,000(1.611)=$16,110DuetoRounding,StoryProblemSolution,Calculationbasedongeneralformula:
FVn=P0(1+i)nFV5=$10,000(1+0.10)5=$16,105.10,Wewillusethe“Rule-of-72”,Quick!
Howlongdoesittaketodouble$5,000atacompoundrateof12%peryear(approx.)?
DoubleYourMoney!
72/12%=6Yearsor72/6years=12%,Assumethatyouneed$1,000in2years.Letsexaminetheprocesstodeterminehowmuchyouneedtodeposittodayatadiscountrateof7%compoundedannually.,PresentValueSingleDeposit(Graphic),012,$1,000,7%,PV1,PV0,GeneralFutureValueFormula:
FVn=PV0(1+i)nFVn=PV0(FVIFi,n)GeneralPresentValueFormula:
PV0=FVn/(1+i)norPV0=FVn(PVIFi,n)-SeeTable2,GeneralPresentValueFormula,PVIFi,nisonTableIIattheendofthebook,ValuationUsingTableII,JulieMillerwantstoknowhowlargeofadeposittomakesothatthemoneywillgrowto$10,000in5yearsatadiscountrateof10%.,StoryProblemExample,012345,$10,000,10%,Calculationbasedongeneralformula:
PV0=FVn/(1+i)nPV0=$10,000/(1+0.10)5=$6,209.21CalculationbasedonTable2:
PV0=$10,000(PVIF10%,5)=$10,000(.621)=$6,210.00DuetoRounding,StoryProblemSolution,Ifyouinvest$1,000today,youwillreceive$3,000inexactly8years.Whatisthecompoundinterestrateimplicitinthissituation?
FVn=PV0(FVIFi,n)(FVIFi,8)=FV8/PV0=3,000/1,000=3i=14.68%,UnknownInterestRate,Howlongwouldittakeforaninvestmentof$1,000togrowto$1,900ifweinvesteditatacompoundannualinterestrateof10percent?
FVn=PV0(FVIFi,n)(FVIF10%,n)=FVn/PV0=1,900/1,000=1.9n=6.72years,UnknownNumberofCompoundingPeriods,Whatisthefuturevalueof$1millioninvestedat10percentfor25years?
FVn=PV0(FVIFi,n)FV25=PV0(FVIF10%,25)=$1,000,000*10.835=$10,835,000,QuickQuiz,Youneed$30,000incashtobuyahouse4yearsfromtoday.Youexpecttoearn5percentonyoursavings.Howmuchdoyouneedtodeposittodayifthisistheonlymoneyyousaveforthispurpose?
PV0=FVn(PVIFi,n)PV0=FV4(PVIF5%,4)=$30,000*0.823=$246,900,Yourfirmhasbeentoldthatitneeds$74,300todaytofunda$120,000expense6yearsfromnow.Whatrateofinterestwasusedinthecomputation?
FVn=PV0(FVIFi,n)(FVIFi,6)=FV6/PV0=120,000/74,300=1.615i=8.3%,OrdinaryAnnuity:
Paymentsorreceiptsoccurattheendofeachperiod.AnnuityDue:
Paymentsorreceiptsoccuratthebeginningofeachperiod.,TypesofAnnuities,AnAnnuityrepresentsaseriesofequalpayments(orreceipts)occurringoveraspecifiednumberofequaldistantperiods.,StudentLoanPaymentsCarLoanPaymentsInsurancePremiumsMortgagePaymentsRetirementSavings,ExamplesofAnnuities,OrdinaryAnnuity,0123,$100$100$100,EndofPeriod1,EndofPeriod2,Today,EqualCashFlowsEach1PeriodApart,EndofPeriod3,AnnuityDue,0123,$100$100$100,BeginningofPeriod1,BeginningofPeriod2,Today,EqualCashFlowsEach1PeriodApart,BeginningofPeriod3,Itisanordinaryannuitywhosepaymentsorreceiptscontinueforever.PVA=R/ITheABSCo.wantstoofferpreferredstockforsaleatapriceof$60ashare.Ifthecompanywantstheirinvestorstoearnatleasta7.5percentrateofreturn,whatistheminimumannualdividendtheywillneedtopaypershare?
R=PVA*i=60*7.5%=$4.5,Perpetuity,FVAn=R(FVIFAi,n)PVAn=R(PVIFAi,n)FVADn=R(FVIFAi,n)(1+i)PVADn=(1+i)(R)(PVIFAi,n)Ristheperiodreceipt,FormulaaboutAnnuities,Whatisthefuturevalueofannualpaymentsof$6,500foreightyearsat12percent?
FVAn=R(FVIFAi,n)FVA8=$6,500*(FVIFA12%,8)=$6,500*12.30=$79,950,ExampleofAnnuit,1.Readproblemthoroughly2.Createatimeline3.Putcashflowsandarrowsontimeline4.DetermineifitisaPVorFVproblem5.DetermineifsolutioninvolvesasingleCF,annuitystream(s),ormixedflow6.Solvetheproblem7.Checkwithfinancialcalculator(optional),StepstoSolveTimeValueofMoneyProblems,JulieMillerwillreceivethesetofcashflowsbelow.WhatisthePresentValueatadiscountrateof10%.,MixedFlowsExample,012345,$600$600$400$400$100,PV0,10%,1.Solvea“piece-at-a-time”bydiscountingeachpiecebacktot=0.2.Solvea“group-at-a-time”byfirstbreakingproblemintogroupsofannuitystreamsandanysinglecashflowgroups.Thendiscounteachgroupbacktot=0.,HowtoSolve?
“Piece-At-A-Time”,012345,$600$600$400$400$100,10%,$545.45$495.87$300.53$273.21$62.09,$1677.15=PV0oftheMixedFlow,“Group-At-A-Time”(#1),012345,$600$600$400$400$100,10%,$1,041.60$573.57$62.10,$1,677.27=PV0ofMixedFlowUsingTables,$600(PVIFA10%,2)=$600(1.736)=$1,041.60$400(PVIFA10%,2)(PVIF10%,2)=$400(1.736)(0.826)=$573.57$100(PVIF10%,5)=$100(0.621)=$62.10,“Group-At-A-Time”(#2),01234,$400$400$400$400,PV0equals$1677.30.,012,$200$200,012345,$100,$1,268.00,$347.20,$62.10,Plus,Plus,JulieMillerwillreceivethesetofcashflowsbelow.WhatisthePresentValueatadiscountrateof7%.(PIECEATATIMEANDGROUPATATIME),SOLVEPROBLEM,012345,$100$500$500$500$500,7%,44,NominalInterestRate,Thisistheannualratethatisquotedbylawthathasnotbeenadjustedforfrequencyofcompounding.Ifinterestiscompoundedmorethatonceayear,theeffectiveinterestratewillbehigherthatthenominalrate.,45,EffectiveAnnualRate(EAR),Thisistheactualratepaid(orreceived)afteradjustingforcompoundingthatoccursduringtheyearIfyouwanttocomparetwoalternativeinvestmentswithdifferentcompoundingperiodsyouneedtocomputetheEARandusethatforcomparison.,46,CompoundingMorethanOnceaYear,FutureValueswithMonthlyCompoundingSupposeyoudeposit$50amonthintoanaccountthathasaninterestrateof12%,basedonmonthlycompounding.Howmuchwillyouhaveintheaccountin1years?
FVn=P0(1+i/m)mnPV0=FVn/(1+i/m)mnFV1=$50(1+12%/12)12*1=$50*1.127=$56.35,47,ContinuousCompounding,SometimesinvestmentsorloansarefiguredbasedoncontinuouscompoundingFVn=PV0(e)in,48,ThingstoRemember,YouALWAYSneedtomakesurethattheinterestrateandthetimeperiodmatch.Ifyouarelookingatannualperiods,youneedanannualrate.Ifyouarelookingatmonthlyperiods,youneedamonthlyrate.,49,EAR-Formula,Rememberthattheiisthequotedratemisthenumberofcompoundingperiodsperyear,Ifasavingsplanofferedanominalinterestrateof8%compoundedquarterlyonaone-yearinvestment,whatstheeffectiveannualinterestrate?
EAR=1+(8%/4)4-1=8.243%,Example,LoanTypesandLoanAmortization,PurediscountloansAborrowerreceivesmoneytodayandrepaysasinglelumpsumatsometimeinthefuture.Interest-onlyloansAborrowerpaysinteresteachperiodandrepaystheentireprincipleatsomepointinthefuture.AmortizedloansAlenderrequirestheborrowertorepaypartsoftheloanamountovertime.,2023/7/2,EssentialsofCorporateFinance,51,Theprocessofpayingoffaloanbymakingregularprinciplereductionsiscalledamortizingtheloan.Installment-typeLoanItisrepaidinequalperiodicpaymentsthatincludebothinterestandprinciple.Thesepaymentscanbemademonthly,quarterly,semiannually,orannually.Commonexamples:
mortgageloans,autoloans,consumerloans,andcertainbusinessloans.,AmortizingaLoan,1.Calculatethepaymentperperiod.2.DeterminetheinterestinPeriodt.(LoanBalanceatt-1)x(i%/m)3.ComputeprincipalpaymentinPeriodt.(Payment-InterestfromStep2)4.DetermineendingbalanceinPeriodt.(Balance-principalpaymentfromStep3)5.StartagainatSte
- 配套讲稿:
如PPT文件的首页显示word图标,表示该PPT已包含配套word讲稿。双击word图标可打开word文档。
- 特殊限制:
部分文档作品中含有的国旗、国徽等图片,仅作为作品整体效果示例展示,禁止商用。设计者仅对作品中独创性部分享有著作权。
- 关 键 词:
- 财务管理英文第十三版ch 3_sheena 财务管理 英文 第十三 ch _sheena